Qinglai Wei

Adaptive Dynamic Programming for Finite-Horizon Optimal Control of Discrete-Time Nonlinear Systems With

In this paper, we study the finite-horizon optimal control problem for discrete-time nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an -error bound. The optimal number of control steps can also be obtained by the proposed ADP algorithms. A convergence analysis of the proposed ADP algorithms in terms of performance index function and control policy is made. In order to facilitate the implementation of the iterative ADP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. Finally, two simulation examples are employed to illustrate the applicability of the proposed method.

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In this paper, a new iterative adaptive dynamic programming (ADP) method is proposed to solve a class of continuous-time nonlinear two-person zero-sum differential games. The idea is to use the ADP technique to obtain the optimal control pair iteratively which makes the performance index function reach the saddle point of the zero-sum differential games. If the saddle point does not exist, the mixed optimal control pair is obtained to make the performance index function reach the mixed optimum. Stability analysis of the nonlinear systems is presented and the convergence property of the performance index function is also proved. Two simulation examples are given to illustrate the performance of the proposed method.

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An intelligent-optimal control scheme for unknown nonaffine nonlinear discrete-time systems with discount factor in the cost function is developed in this paper. The iterative adaptive dynamic programming algorithm is introduced to solve the optimal control problem with convergence analysis. Then, the implementation of the iterative algorithm via globalized dual heuristic programming technique is presented by using three neural networks, which will approximate at each iteration the cost function, the control law, and the unknown nonlinear system, respectively. In addition, two simulation examples are provided to verify the effectiveness of the developed optimal control approach.

An iterative adaptive dynamic programming method for solving a class of nonlinear zero-sum differential games

In this paper, a finite-horizon neuro-optimal tracking control strategy for a class of discrete-time nonlinear systems is proposed. Through system transformation, the optimal tracking problem is converted into designing a finite-horizon optimal regulator for the tracking error dynamics. Then, with convergence analysis in terms of cost function and control law, the iterative adaptive dynamic programming (ADP) algorithm via heuristic dynamic programming (HDP) technique is introduced to obtain the finite-horizon optimal tracking controller which makes the cost function close to its optimal value within an @?-error bound. Three neural networks are used as parametric structures to implement the algorithm, which aims at approximating the cost function, the control law, and the error dynamics, respectively. Two simulation examples are included to complement the theoretical discussions.

Optimal control of unknown nonaffine nonlinear discrete-time systems based on adaptive dynamic programming

The optimization of energy consumption, with consequent costs reduction, is one of the main challenges in present and future smart grids. Of course, this has to occur keeping the living comfort for the end-user unchanged. In this work, an approach based on the mixed-integer linear programming paradigm, which is able to provide an optimal solution in terms of tasks power consumption and management of renewable resources, is developed. The proposed algorithm yields an optimal task scheduling under dynamic electrical constraints, while simultaneously ensuring the thermal comfort according to the user needs. On purpose, a suitable thermal model based on heat-pump usage has been considered in the framework. Some computer simulations using real data have been performed, and obtained results confirm the efficiency and robustness of the algorithm, also in terms of achievable cost savings.

Finite-horizon neuro-optimal tracking control for a class of discrete-time nonlinear systems using adaptive dynamic programming approach

In this paper, a novel data-driven stable iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal temperature control problems for water-gas shift (WGS) reaction systems. According to the system data, neural networks (NNs) are used to construct the dynamics of the WGS system and solve the reference control, respectively, where the mathematical model of the WGS system is unnecessary. Considering the reconstruction errors of NNs and the disturbances of the system and control input, a new stable iterative ADP algorithm is developed to obtain the optimal control law. The convergence property is developed to guarantee that the iterative performance index function converges to a finite neighborhood of the optimal performance index function. The stability property is developed to guarantee that each of the iterative control laws can make the tracking error uniformly ultimately bounded (UUB). NNs are developed to implement the stable iterative ADP algorithm. Finally, numerical results are given to illustrate the effectiveness of the developed method.

Optimal Home Energy Management Under Dynamic Electrical and Thermal Constraints

In this paper, a novel heuristic dynamic programming (HDP) iteration algorithm is proposed to solve the optimal tracking control problem for a class of nonlinear discrete-time systems with time delays. The novel algorithm contains state updating, control policy iteration, and performance index iteration. To get the optimal states, the states are also updated. Furthermore, the “backward iteration” is applied to state updating. Two neural networks are used to approximate the performance index function and compute the optimal control policy for facilitating the implementation of HDP iteration algorithm. At last, we present two examples to demonstrate the effectiveness of the proposed HDP iteration algorithm.

Data-Driven Neuro-Optimal Temperature Control of Water–Gas Shift Reaction Using Stable Iterative Adaptive Dynamic Programming

In this paper, we establish a new data-based iterative optimal learning control scheme for discrete-time nonlinear systems using iterative adaptive dynamic programming (ADP) approach and apply the developed control scheme to solve a coal gasification optimal tracking control problem. According to the system data, neural networks (NNs) are used to construct the dynamics of coal gasification process, coal quality and reference control, respectively, where the mathematical model of the system is unnecessary. The approximation errors from neural network construction of the disturbance and the controls are both considered. Via system transformation, the optimal tracking control problem with approximation errors and disturbances is effectively transformed into a two-person zero-sum optimal control problem. A new iterative ADP algorithm is then developed to obtain the optimal control laws for the transformed system. Convergence property is developed to guarantee that the performance index function converges to a finite neighborhood of the optimal performance index function, and the convergence criterion is also obtained. Finally, numerical results are given to illustrate the performance of the present method.

Optimal Tracking Control for a Class of Nonlinear Discrete-Time Systems With Time Delays Based on Heuristic Dynamic Programming

In this paper, a new iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for infinite horizon discrete-time nonlinear systems with finite approximation errors. First, a new generalized value iteration algorithm of ADP is developed to make the iterative performance index function converge to the solution of the Hamilton-Jacobi-Bellman equation. The generalized value iteration algorithm permits an arbitrary positive semi-definite function to initialize it, which overcomes the disadvantage of traditional value iteration algorithms. When the iterative control law and iterative performance index function in each iteration cannot accurately be obtained, for the first time a new “design method of the convergence criteria” for the finite-approximation-error-based generalized value iteration algorithm is established. A suitable approximation error can be designed adaptively to make the iterative performance index function converge to a finite neighborhood of the optimal performance index function. Neural networks are used to implement the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the developed method.

Adaptive Dynamic Programming for Optimal Tracking Control of Unknown Nonlinear Systems With Application to Coal Gasification

This paper is concerned with a new iterative θ-adaptive dynamic programming (ADP) technique to solve optimal control problems of infinite horizon discrete-time nonlinear systems. The idea is to use an iterative ADP algorithm to obtain the iterative control law which optimizes the iterative performance index function. In the present iterative θ-ADP algorithm, the condition of initial admissible control in policy iteration algorithm is avoided. It is proved that all the iterative controls obtained in the iterative θ-ADP algorithm can stabilize the nonlinear system which means that the iterative θ-ADP algorithm is feasible for implementations both online and offline. Convergence analysis of the performance index function is presented to guarantee that the iterative performance index function will converge to the optimum monotonically. Neural networks are used to approximate the performance index function and compute the optimal control policy, respectively, for facilitating the implementation of the iterative θ-ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the established method.